The coalescent of a sample from a linear-fractional branching process

Natalia Cardona-Tobón; Sandra Palau

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arXiv · 2506.17470

The coalescent of a sample from a linear-fractional branching process

Natalia Cardona-Tobón·Sandra Palau

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Abstract

In this article, we focus on Bienaym\'e-Galton-Watson processes with linear-fractional offspring distributions. At a fixed generation, we consider a sample of the individuals alive, drawn in two different ways: either through Bernoulli sampling, where each individual is selected independently with a given probability, or through uniform sampling, where a fixed number of individuals are chosen uniformly at random. We analyze the genealogical trees generated by the sampled individuals. In particular, we establish a relationship between the distributions of the trees resulting from the two sampling schemes.

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Natalia Cardona-Tobón, Sandra Palau. 2025-06-20. The coalescent of a sample from a linear-fractional branching process. https://arxiv.org/abs/2506.17470

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